I am positive means I'm certain. It's usually used when there is reason to express certainty in some statement.
So, you could say:
— Do you think it will be cold tomorrow?
— I'm positive!
— It's cold today.
— I'm positive.
Here are some other questions that might be followed by I'm positive:
- Are you sure it's safe?
- Are you capable of delivering the product on time?
- Are [sports team name] going to win tonight?
- Do you think the weather will be good enough for a picnic on Saturday?
- Did John understand the requirements?
Notice that not all of them ask whether the person is sure, but they do all require the respondent to make some kind of judgement, which is why it is possible to respond with "I'm positive"; it's expressing the degree of certainty in that judgement.
This is slightly different. Normally, the answer to this, if you bought bananas, would simply be "Yes". However, there is a context in which you might say "I'm positive" - basically if there's some reason to not be certain of the result. For example, person A goes to the fruit bowl (where there are no bananas, despite asking person B to buy some) and says, "Did you buy bananas?" Then person B looks in the fruit bowl, looks in the shopping bag, glances all around the room and says, "I'm positive I bought them!" before finally finding them in the cupboard.
N.B. There is also another meaning of I'm positive that would be apparent in a different context - namely if you have been tested for something.
For example, I was tested for HIV and I'm positive. That means that the speaker is HIV-positive.